The hysteresis and eddy current losses in a d.c. machine running m 1000 r.p.m. are 250W and 100W respectively. If the flux remains constant at what speed will be total iron losses be halved?

Question

Answer

Calculation of Speed for Halving Total Iron Losses in a DC Machine

Given Information:

Hysteresis loss = 250 W

Eddy current loss = 100 W

Total iron loss = 250 W + 100 W = 350 W

Flux remains constant

Initial speed = 1000 rpm

Solution:

Let's assume that at a certain speed 'n' the total iron losses will be halved i.e. 350/2 = 175 W.

Now, we know that:

Total iron loss = Hysteresis loss + Eddy current loss

Hysteresis loss is directly proportional to frequency (n)

Eddy current loss is proportional to the square of frequency (n^2)

Therefore, we can write:

250 α n

100 α n^2

Dividing the above two equations, we get:

250/100 α n/n^2

2.5 α 1/n

n α 1/2.5

n = 400 rpm

Therefore, the speed at which the total iron losses will be halved is 400 rpm.

Explanation:

Hysteresis loss is caused by the reversal of magnetic domains in the iron core and is directly proportional to the frequency of the magnetic field. Eddy current loss is caused by the circulating currents in the iron core due to the alternating magnetic field and is proportional to the square of the frequency. Thus, as the speed of the DC machine increases, both the hysteresis and eddy current losses increase, resulting in an increase in the total iron losses. In order to reduce the total iron losses, the speed of the machine needs to be reduced. In this case, we have calculated the speed at which the total iron losses will be halved by equating the total iron losses at the initial speed to half of the total iron losses at the new speed. We have then used the equations for hysteresis and eddy current losses to calculate the new speed.

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